Heat the oil in a heavy large skillet over medium heat. Add the onion and sauté until beginning to softer, about 4 minutes. Add the squash slices and sprinkle with salt and black pepper. Sauté until the squash softens, about 10 minutes. Sprinkle with the red pepper flakes and stir.
Meanwhile, add the pasta to a large pot of boiling salted water and stir. Return the water to a boil and cook until the pasta is tender but still firm to the bite, stirring occasionally. I start checking 2 minutes before the time suggested on the package. Reserve 1 cup of the pasta cooking water, and then drain the pasta.
Add the pasta to the skillet with the squash. Add ⅓ cup of the pesto and stir to coat. Add ½ cup of the Parmesan. Add enough pasta cooking liquid to loosen the texture. Season to taste with salt and pepper.
Serve the pasta, offering more cheese to sprinkle on top.